Chapter 4.1, Problem 5PP

To determine

To calculate: the efficiency of the machine.

Answer to Problem 5PP

The machine is $\underset{\_}{40\text{ \%}}$ efficient.

Explanation of Solution

Given data:

Input work, $W_{in}=2000\text{ J}$

Output work, $W_{out}=800\text{ J}$

Formula used:

Efficiency Equation:

  $e=\frac{W_{out}}{W_{in}}\times 100$

Where $e$ is efficiency of machine (as percentage), $W_{in}$ is the input work in joules and $W_{out}$ is the output work in joules.

Calculation:

As per the problem,

  $\begin{array}{l}{W}_{in}=2000\text{ J}\\ W_{out}=800\text{ J}\end{array}$

Substitute the values of input and output work in the efficiency equation:

  $\begin{array}{l}e=\frac{W_{out}}{W_{in}}\times 100\\ e=\frac{800\text{ J}}{2000\text{ J}}\times 100\\ e=40\%\end{array}$

Conclusion:

The machine is $\underset{\_}{40\text{ \%}}$ efficient.